Brutal snowstorms, an upheaval in Boston city politics, a contentious tax debate on Beacon Hill, and now terrorism at the Marathon. Since nearly the opening hours of the race to fill John Kerry’s US Senate seat, a series of events has smothered the campaign and raised serious questions over the efficacy of special elections.

For three months, the candidates — two Democrats and three Republicans — have been crisscrossing the state, airing commercials, and raising money, hoping to gain voters’ attention.

But they have found little success. With the primary election looming on Tuesday, the public appears to have barely taken notice. Despite several televised debates and a flurry of media coverage, the race has lacked the sort of robust and spirited discussions of issues and the vetting of candidates that has historically distinguished Massachusetts Senate campaigns.

Analysts cite a host of reasons: the inability of the candidates in either party to swiftly generate voter enthusiasm; the string of news and weather events in the last few months that consumed the media’s and public’s interest; and the voters’ fatigue after a year of intense politicking.

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The sputtering race and the prospect that it will lure few people to the polls to fill such an important political position has prompted some strong criticism of the truncated special election system that Democrats created in 2004 to fill vacant US Senate seats.

“It’s no one’s idea of a functioning democracy,’’ said Thomas J. Whalen, a political historian and associate professor of social sciences at Boston University. “If the weather interferes, or there’s an act of God, or this tragedy we just experienced at the Marathon, it throws everything off base. It’s like a house of cards, one little thing will cause the electoral process to collapse.’’

Evidence that the campaign has not captured voter interest can be found in the early requests for absentee balloting, prompting the state’s top election official to predict a low turnout.

“These are abysmal numbers,’’ said Secretary of State William F. Galvin, citing the fact that applications are running about 25 percent the level in the primary for the 2010 special election. “It is depressing to see. There seems to be no momentum to the election.”

Barry Chin/Globe Staff

Analysts say Stephen Lynch (left) could have used more time and public attention against Edward J. Markey.

Other experienced observers of state politics agree. “This is like a race that didn’t happen,’’ said Gregory Torres, president of MassInc, a nonpartisan think tank that has in the past sponsored debates in statewide political races. “This is a United States Senate seat, for God’s sake. We need to have a much more vigorous debate and examination of the candidates and the issues.’’

In their last weekend before primary day, the candidates raced to make up for lost time, packing their schedules and sprinting across the state to meet voters at dozens of events.

But most acknowledged the attention deficit they face.

“So many of the voters are still trying to grasp what happened last week, and aren’t thinking about politics,” Lynch said after an event in Worcester on Saturday afternoon.

In an overtly political move, a coalition of Democratic leaders concocted the special election process in 2004, when Kerry was the Democratic presidential nominee. To prevent Republican Governor Mitt Romney from handpicking Kerry’s Senate replacement, the Democratic Legislature changed state law to establish a special election process to fill a vacancy.

Democrats were confident they could win a special election if Kerry won his race against President George W. Bush.

That calculation that Democrats would have a clear advantage in a special election proved embarrassingly false several years later when Scott Brown, a little-known Republican state senator, won a special election in January 2010 to fill the seat long held by the late Edward M. Kennedy.

Under the 2004 law, the election must take place no sooner than 145 days and no later than 160 days after the vacancy is created — a tight campaign schedule that can easily be overwhelmed by other events.

During a normal election cycle, races for state constitutional offices and the US Senate take place over months, or possibly several years, giving candidates and their staff time to build organizations, polish their campaign skills, and create a strong profile. Scott Brown and Elizabeth Warren did battle for more than a year before the November 2012 election.

The shorter election cycle has the greatest impact on candidates who have low voter identification, few resources, and are not heavily tied into the party apparatus or leadership that can be critical in a primary.

Analysts agree that Democrat Stephen Lynch, the South Boston congressman who is already facing an uphill primary fight, could have used more time and public attention to gain traction to overtake front-runner, Edward J. Markey, a veteran congressman.

On the Republican side, state Representative Daniel B. Winslow of Norfolk and political newcomer Gabriel Gomez, a Cohasset businessman, are also facing the same problem as they try to challenge the GOP’s perceived front-runner, Michael J. Sullivan, a former federal and state prosecutor and one-time state legislator.

Jeffrey M. Berry, a political science professor at Tufts University, said Winslow, with his energetic effort to bring new approaches to the Republican Party, is a good example of how the truncated election process works against candidates who could be more viable in a longer campaign.

“Of the Republicans, Winslow has to be most disappointed,’’ said Berry. “He has a good reputation in the state Legislature and among the party faithful but can’t get the recognition outside the political world.’’

That analysis underscores what other critics say is the ability of insiders and activists in both parties to dominate a special election and effectively choose who will fill such a critical public office in a low turnout elections.

Jerold Duquette, associate professor of political science at Central Connecticut State University, thinks gubernatorial appointment to fill the seat is far preferable than holding elections that draw little interest or participation. He suggests that the state should examine going back to the system in place prior to 2004, in which the governor would appoint a senator until the next regular state election.

“Having a system with a gubernatorial appointment for two years and then a campaign is not perfect, but having a longer debate is a much better deal,’’ Duquette said. “What’s in place now is not good for democracy or a competitive election.’’

But others dismiss those arguments, saying the special election process is far better than allowing a governor to make the decision.

“A flawed campaign that allows the voters to decide who will be the senator is a lot better than having one person, the governor, filling the position,’’ said former Republican state treasurer Joseph D. Malone.

Pam Wilmot, the executive director of Common Cause of Massachusetts, said her group’s initial support of the law to create special elections for the US Senate remains unchanged despite what she acknowledges have been “a string of disastrous events that has fully absorbed the public’s and media’s attention.’’

“If you give the governor the appointment for two years, it makes it very difficult to unseat that person,’’ Wilmot said. “Incumbents have all the privileges and benefits of incumbency that accrues to an enormous extent over a two-year period.’’

State Representative William M. Straus, a Mattapoisett Democrat and one of the architects of the law, agrees.

“There is no impediment to registered voters to participate in making the decisions,’’ he said. “If they don’t turn out, it is a shame, but I don’t blame the fact we are holding the election as the problem.’’

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